The Scaling Law between Electron Time-of-Flight Distances and Loop Lengths in Solar Flares

This is the authors' abstract. We don't add key points for this paper.

From the complete data set of solar flares simultaneously observed with the Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory (CGRO) in the high-time resolution mode (64 ms) and the Hard X-ray Telescope (HXT) on board Yohkoh, we were able to determine the electron time-of-flight (TOF) distance l' and the flare loop geometry in 42 events. The electron TOF distances were determined from time delays (of ≈ 10-100 ms) of hard X-ray (HXR) pulses (measured in 16 channel spectra over ≈ 20-200 keV), produced by the velocity difference of the HXR-producing electrons. The flare loops were mostly identified from double footpoint sources in ≥30 keV HXT images, with radii in the range r = 3000-25,000 km. We find a scaling law between the electron TOF distance l' and the flare loop half-length 5 = r(π/2), having a mean ratio (and standard deviation) of l'/s = 1.4±0.3. In five flares, we observe coronal ≥ 30 keV HXR sources of the Masuda type in the cusp region above the flare loop and find that their heights are consistent with the electron TOF distance to the footpoints. These results provide strong evidence that particle acceleration in solar flares occurs in the cusp region above the flare loop and that the coronal HXR sources discovered by Masuda et al. are a signature of the acceleration site, probably controlled by a magnetic reconnection process.